Comparison between rigid syntomic and crystalline syntomic cohomology for strictly semistable log schemes with boundary

Abstract

We introduce rigid syntomic cohomology for strictly semistable log schemes over a complete discrete valuation ring of mixed characteristic (0,p). In case a good compactification exists, we compare this cohomology theory to Nekov\'a\v{r}-Nizio{\l}'s crystalline syntomic cohomology of the generic fibre. The main ingredients are a modification of Gro{\ss}e-Kl\"onne's rigid Hyodo-Kato theory and a generalisation of it for strictly semistable log schemes with boundary.